On the Generalized Ornstein-Uhlenbeck Semigroup
Mostafa Maslouhi, El houssain Lamine
TL;DR
This paper establishes new functional inequalities for the Ornstein-Uhlenbeck semigroup within the Dunkl operators framework, leading to Sobolev-logarithmic and hypercontractivity results that extend classical analysis tools.
Contribution
It introduces generalized functional inequalities for the Ornstein-Uhlenbeck semigroup in the Dunkl setting, advancing the understanding of its analytical properties.
Findings
Derived Sobolev-logarithmic inequalities.
Proved hypercontractivity properties.
Extended classical inequalities to Dunkl operators.
Abstract
We give several functional inequalities related to the Ornstein-Uhlenbeck semigroup in the Dunkl differential-difference operators setting. As an application of these inequalities, we derive out a Sobolev-logarithmic and an hypercontractivity properties for this semigroup
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Spectral Theory in Mathematical Physics · Quantum Mechanics and Non-Hermitian Physics